A widely-used technique for processing and analyzing electrical signals, as well as other phenomena and data, is Fourier analysis. Generally, Fourier spectral analysis provides a technique for examining global energy-frequency distributions. Fourier analysis is in some respects quite limited, however. Even though Fourier transform is valid under very general conditions, Fourier spectral analysis requires that a system be linear and that the data analyzed be strictly periodic or stationary. (See, e.g., N. E. Huang, et al., “The Empirical Mode Decomposition and The Hilbert Spectrum for Nonlinear and Non-stationary Time Series Analysis,” Proc. R. Soc. Lond. A. (1998) 454, 903-995.)
Other techniques for processing and analyzing non-stationary data have been developed. These techniques include the spectrogram method, wavelet analysis, the Wigner-Ville distribution (also referred to as the Heisenberg wavelet), the evolutionary spectrum, and the empirical orthogonal function expansion. Typically, though, these techniques supplement, but still depend on, Fourier analysis. Accordingly, when applied to nonlinear systems, they can yield limited or even misleading results.
A context in which these traditional techniques are frequently inadequate is with respect to estimation time-varying distorted voltage and current signals. Accurate estimation of such signals is needed for determining innovative power quality indices and thresholds corresponding to electrical power systems, for example, as well as for determining equipment derating levels and for devising adequate mitigation methods, including harmonic filter designs.
In the context of estimating time-varying distorted signals, such as voltage and current signals generated with modem power systems, it is not appropriate to use harmonics (multiples of a sinusoidal wave) for describing the higher modes of oscillations that may be present in non-stationary and nonlinear waveform distortions. Harmonics imply stationarity and linearity among the modes of oscillations.
Moreover, in the specific context of estimating time-varying modes in distorted voltage and current signals, other factors must be taken into account. These factors include the relative smallness of the distortions magnitudes, typically ranging from 1-10% of the fundamental frequency for voltage and 10-30% of the fundamental frequency for current. Another factor is that the fundamental frequency may not be constant during periods of observation of the signals, which can result from load fluctuations and system transients. Still another factor is that the typical distortion frequencies of interest in electric power quality analysis may lie within an octave of one another, thus posing a separation challenge.
Accordingly, there is a need for more effective and efficient methods for processing and analyzing time-varying waveforms such as those corresponding to time-varying distorted voltage and current signals. One proposed technique for processing and analyzing non-stationary signals is the Hilbert-Huang (HH) method, which employs empirical mode decomposition (EMD). EMD, however, does not separate frequencies that lie within an octave of one another, which as already noted can be of particular concern in the context of electric power quality analysis. One proposed technique for improving EMD is to employ a masking signal to enhance the filtering capabilities of EMD. To date, however, there is not an effective and efficient technique for choosing appropriate masking signals to use in conjunction with the application of EMI. More particularly, there is not an effective and efficient technique for choosing masking signals that will ensure that application of END generates truly mono-component intrinsic mode functions (IMF)
Accordingly, there is yet a need for a technique to enhance the use of EMD, particularly in context of analyzing time-varying distorted voltage and current signals, by generating appropriate masking signals. There is also a need for a technique for demodulating IMFS obtained by applying EMD.